The Parisi ultrametricity conjecture

• 成果类型: Article
• 署名作者: Panchenko, Dmitry
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.177.1.8
• 发表日期: 2013
• 页码: 383-393
• 关键词: ghirlanda-guerra identities; spin-glass phase; MODEL; systems

摘要

In this paper we prove that the support of a random measure on the unit ball of a separable Hilbert space that satisfies the Ghirlanda-Guerra identities must be ultrametric with probability one. This implies the Parisi ultrametricity conjecture in mean-field spin glass models, such as the Sherrington-Kirkpatrick and mixed p-spin models, for which Gibbs measures are known to satisfy the Ghirlanda-Guerra identities in the thermodynamic limit.